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Number Theory Level 3

15 years ago, A and B were in love. A asked forB's phone number.

A:Hi darling. Whats yr phone no.?

B:Unless you prove to me you are a true mathematician.

A: I'll do anything for you honey.

B:My phone number has 4 digits abcd. \( {(\overline { ab } ) }^{ 2 }+{ (\overline { cd } ) }^{ 2 }={ \overline { abcd }} \). Pls note that abcd is a number not a product. And abcd is the smallest solution.

A:Further detail?

B:No more. I love you honey.

A:I love you too

Find the value of abcd.


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